---coding by yuangu(lifulinghan@aol.com)

--用于計算2個pgs之間的距離

function computeDistance(lat1, lon1,

lat2, lon2)

-- Based on http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf

-- using the "Inverse Formula" (section 4)

local MAXITERS = 20;

-- Convert lat/long to radians

lat1 = math.rad(lat1); -- lat1 * math.pi / 180.0;

lat2 = math.rad(lat2); --lat2 * math.pi / 180.0;

lon1 = math.rad(lon1); --lon1 * math.pi / 180.0;

lon2 = math.rad(lon2); --lon2 * math.pi / 180.0;

local a = 6378137.0; -- WGS84 major axis

local b = 6356752.3142; -- WGS84 semi-major axis

local f = (a - b) / a;

local aSqMinusBSqOverBSq = (a * a - b * b) / (b * b);

local L = lon2 - lon1;

local A = 0.0;

local U1 = math.atan((1.0 - f) * math.tan(lat1));

local U2 = math.atan((1.0 - f) * math.tan(lat2));

local cosU1 = math.cos(U1);

local cosU2 = math.cos(U2);

local sinU1 = math.sin(U1);

local sinU2 = math.sin(U2);

local cosU1cosU2 = cosU1 * cosU2;

local sinU1sinU2 = sinU1 * sinU2;

local sigma = 0.0;

local deltaSigma = 0.0;

local cosSqAlpha = 0.0;

local cos2SM = 0.0;

local cosSigma = 0.0;

local sinSigma = 0.0;

local cosLambda = 0.0;

local sinLambda = 0.0;

local lambda = L; -- initial guess

for iter = 0, MAXITERS - 1 do

local lambdaOrig = lambda;

cosLambda = math.cos(lambda);

sinLambda = math.sin(lambda);

local t1 = cosU2 * sinLambda;

local t2 = cosU1 * sinU2 - sinU1 * cosU2 * cosLambda;

local sinSqSigma = t1 * t1 + t2 * t2;

sinSigma = math.sqrt(sinSqSigma);

cosSigma = sinU1sinU2 + cosU1cosU2 * cosLambda;

sigma = math.atan2(sinSigma, cosSigma);

local sinAlpha = 0.0

if (sinSigma ~= 0) then

sinAlpha = cosU1cosU2 * sinLambda / sinSigma

end

cosSqAlpha = 1.0 - sinAlpha * sinAlpha;

cos2SM = 0.0

if cosSqAlpha ~= 0 then

cos2SM = cosSigma - 2.0 * sinU1sinU2 / cosSqAlpha;

end

local uSquared = cosSqAlpha * aSqMinusBSqOverBSq;

A = 1 + (uSquared / 16384.0) *

(4096.0 + uSquared *

(-768 + uSquared * (320.0 - 175.0 * uSquared)));

local B = (uSquared / 1024.0) *

(256.0 + uSquared *

(-128.0 + uSquared * (74.0 - 47.0 * uSquared)));

local C = (f / 16.0) *

cosSqAlpha *

(4.0 + f * (4.0 - 3.0 * cosSqAlpha));

local cos2SMSq = cos2SM * cos2SM;

deltaSigma = B * sinSigma *

(cos2SM + (B / 4.0) *

(cosSigma * (-1.0 + 2.0 * cos2SMSq) -

(B / 6.0) * cos2SM *

(-3.0 + 4.0 * sinSigma * sinSigma) *

(-3.0 + 4.0 * cos2SMSq)));

lambda = L +

(1.0 - C) * f * sinAlpha *

(sigma + C * sinSigma *

(cos2SM + C * cosSigma *

(-1.0 + 2.0 * cos2SM * cos2SM)));

local delta = (lambda - lambdaOrig) / lambda;

if (math.abs(delta) < 1.0e-12) then

break;

end

end

return b * A * (sigma - deltaSigma);

end

--for test

print(computeDistance(34.8082342, 113.6125439, 34.8002478, 113.659779))

總結

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